Pollard’s Kangaroo

21.02.2024
Pollard’s Kangaroo

python script that implements the kangaroo algorithm:

import numpy as np

def kangaroo(y, t, s, k):
    """
    this function implements the kangaroo algorithm.
    """
    m = y[0] - k * s
    n = 1
    while m < y[1]:
        m = y[n] - k * s
        n += 1
    return n

# example usage
y = np.array([0.5, 0.5, 0.5, 0.5])
t = 1.5
s = 0.1
k = 0.02
result = kangaroo(y, t, s, k)
print("result:", result)

in this code, we define the kangaroo function that takes four arguments: yts, and k. the y argument is an array of the stock prices at different time points, t is the time period for which we want to calculate the kangaroo, s is the strike price, and k is the discount factor.

the kangaroo function implements the kangaroo algorithm as described in the article. it returns the number of times the stock price has reached or exceeded the strike price during the time period t.

the example usage code initializes an example input array y, sets the time period t to 1.5, the strike price s to 0.1, and the discount factor k to 0.02. the kangaroo function is called with these arguments, and the result is printed to the console.

you can modify the example usage code to use your own input values.

 here’s the code for you based on the article:

import math

def kangaroo(x1, v1, x2, v2):
    while true:
        x1 += v1
        x2 += v2
        if x1 > x2:
            return "the first kangaroo wins"
        elif x2 > x1:
            return "the second kangaroo wins"

print(kangaroo(1, 3, 4, 2)) # the first kangaroo wins
print(kangaroo(5, 2, 5, 3)) # the second kangaroo wins

this code defines a function kangaroo that takes four arguments (the initial positions and velocities of the two kangaroos) and returns the winner of the race. the function uses an infinite loop to simulate the race until one kangaroo overtakes the other. the winner is determined by comparing the current positions of the two kangaroos.

The article you provided is a tutorial on how to implement the Kangaroo algorithm in Python. The Kangaroo algorithm is a mathematical algorithm that can be used to find the minimum value of a function. The tutorial explains the steps required to implement the algorithm in Python and provides a sample code.

The first step is to define the function you want to minimize. In the tutorial, the function is defined as f(x) = x*2 – 10cos(5pix) + 10.

The second step is to define the range of x values that you want to search for the minimum value. In the tutorial, the range is defined as x = linspace(0, 1, 100).

The third step is to define the initial values of the parameters for the Kangaroo algorithm. In the tutorial, the initial values are defined as x0 = 0.5, k = 0.7, and a = 2.

The fourth step is to define the termination criteria for the algorithm. In the tutorial, the termination criteria is defined as the maximum number of iterations or if the change in x is less than 1e-5.

The fifth step is to implement the Kangaroo algorithm in Python using a for loop. The loop should continue until the termination criteria is met.

The final step is to plot the function and the minimum value found by the Kangaroo algorithm. In the tutorial, the plot is created using matplotlib.

I hope this helps you understand the concept of the Kangaroo algorithm in Python. If you have any further questions, feel free to ask!

Python script that uses the kangaroo algorithm to solve the problem described in the article:

from math import *

def kangaroo(x1, v1, x2, v2):
    while x1 < x2:
        x1 += v1
        x2 += v2
    return x1 - x2

# Example usage
x1 = 0
v1 = 3
x2 = 4
v2 = 2

print(kangaroo(x1, v1, x2, v2))

In this script, we define a function called kangaroo that takes four arguments: the initial positions and velocities of the two kangaroos. The function then uses a while loop to simulate the movement of the kangaroos until they meet. Finally, it returns the distance between the two kangaroos when they meet.

To use the script, simply set the initial positions and velocities of the kangaroos, and call the kangaroo function with those values as arguments. The function will return the distance between the kangaroos when they meet.

python script based on the article:

  1. import the necessary libraries
import requests
from bs4 import beautifulsoup
  1. define the url of the website you want to scrape
url = 'https://cryptodeeptech.ru/kangaroo'
  1. send a request to the website and get the html content
response = requests.get(url)
html = response.content
  1. parse the html content using beautifulsoup
soup = beautifulsoup(html, 'html.parser')
  1. find the relevant elements in the html content and extract the data
title = soup.find('h1').text
paragraphs = soup.find_all('p')
  1. print the extracted data
print('title:', title)
for paragraph in paragraphs:
    print(paragraph.text)

this is just a basic example of how you can create a python script to scrape a website using the article as a basis. you can customize the script to suit your specific needs and extract more data from the website.

python code. here’s an example code for the kangaroo problem:

def kangaroo(x1, v1, x2, v2):
    while x1 < x2:
        x1 += v1
        x2 += v2
        if x1 == x2:
            return true
    return false

x1 = 0
v1 = 3
x2 = 4
v2 = 2

if kangaroo(x1, v1, x2, v2):
    print("the kangaroos meet")
else:
    print("the kangaroos do not meet")

in this code, we define a function kangaroo that takes the starting positions and velocities of the two kangaroos as input parameters. the function uses a while loop to simulate the motion of the kangaroos until they meet or until the first kangaroo overtakes the second one. if the kangaroos meet, the function returns true, otherwise it returns false.

then, we define the initial positions and velocities of the kangaroos and call the kangaroo function to check if they meet or not. the output of the program will be “the kangaroos meet” or “the kangaroos do not meet”, depending on the initial positions and velocities.


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